Find the line of best fit for the given data.
\[
(4,0),(5,7),(6,9),(7,9)
\]

Step 1 ：We are given the data points (4,0),(5,7),(6,9),(7,9). We need to find the line of best fit for these points.

Step 2 ：The line of best fit, also known as the regression line, is a line that is used in the fields of statistics and mathematics to represent the best estimate of a scatter plot of data points. The line of best fit is determined by the method of least squares, which minimizes the sum of the squares of the residuals (the differences between the observed and estimated values).

Step 3 ：The formula for the line of best fit is given by: \(y = mx + c\)

Step 4 ：Where: \(m\) is the slope of the line, given by the formula \(\frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{n(\Sigma x^2) - (\Sigma x)^2}\), \(c\) is the y-intercept of the line, given by the formula \(\frac{(\Sigma y) - m(\Sigma x)}{n}\), \(n\) is the number of data points, \(\Sigma\) denotes the sum of the values.

Step 5 ：We can calculate the slope and y-intercept using these formulas and then form the equation of the line of best fit.

Step 6 ：Given x = [4 5 6 7], y = [0 7 9 9], n = 4, sum_x = 22, sum_y = 25, sum_xy = 152, sum_x2 = 126.

Step 7 ：Calculating the slope (m) gives us 2.9 and calculating the y-intercept (c) gives us -9.7.

Step 8 ：The slope and y-intercept of the line of best fit for the given data points are 2.9 and -9.7 respectively. Therefore, the equation of the line of best fit is \(y = 2.9x - 9.7\).

Step 9 ：Final Answer: The line of best fit for the given data is \(\boxed{y = 2.9x - 9.7}\).